Elastic, optoelectronic and photocatalytic properties of semiconducting CsNbO3: first principles insights

The cubic phase of CsNbO3 (CNO) perovskite has been hypothesized to investigate the elastic, electronic, photocatalytic, and optical properties for various technological applications using first-principles method. The pressure dependent structural stability has been confirmed from computed elastic constants. Relatively high value of elastic moduli, large hardness and toughness suggested that CNO would be applicable to design industrial machineries. The ductile to brittle transition is noticed at 20 GPa. The indirect bandgap of CNO proclaims its suitability for photovoltaic and IR photodetector applications. The total and partial density of states are calculated to show in evidence the contribution of individual atomic orbitals in the formation of bands. The pressure changes orbitals hybridization which can be substantiated by the change in the bandgap. Strong covalency of the Nb–O bond and antibonding character of Cs–O have been anticipated by the Mulliken population analysis and by the contour maps of electron charge density. The low carrier effective mass and high mobility carriers predict the good electrical conductivity of the material. The calculated values of conduction and valance band edge potential illustrate the excellent water-splitting and environmental pollutants degradation properties of CNO.

www.nature.com/scientificreports/ the expansion of light response ranges should therefore be the main research areas for oxide photocatalysts 13 . For the construction of lasers and detectors, many semiconducting materials are used 16 . Recent researches have shown the structural, magnetic, and magnetocaloric properties of niobates under pressure 17 . Materials must be customized for individual application since their qualities determine how effective they are in field service. Nowadays, many theoretical investigations have been performed on niobate oxides such as LiNbO 3 , NaNbO 3 , KNbO 3 , SrNbO 3 , and RbNbO 3 18 , RbSr 2 Nb 3 O 10 19 etc. as well as the temperature-dependent investigations of different properties of CsNbO 3 have also been demonstrated 17 . These explorations are proved to be essential to the material engineering sectors. These oxides exhibit structural phase transitions at various pressures 20 and have a high dielectric constant 21 , high breakdown strength 22 , wide bandgap 23 , and low current leakage current density 24 . As a function of temperature, pressure, and particle size, NaNbO 3 displays a very intricate sequence of structural phase changes 25 . Under light illumination, KNbO 3 is very stable and nontoxic 26 . Due to its accessibility, low toxicity, and ability to exhibit strong polarization at high electric fields, AgNbO 3 27 is another alluring leadfree ferroelectric material. Cs shows the greater ionic radius, low first ionization energy, and electronegativity, while relatively average density and melting temperature among the A-site cations of niobates. Therefore, in the current study, we choose CsNbO 3 (CNO) for additional pressure dependent analysis among different niobates. Very recently, pressure dependent vibrational, electronic, thermoelectronic, and optical properties of CNO have been reported 28 . However, the value of reported energy gap was quite low due to the use of conventional exchange correlational functional 28 . Despite the fact of very intriguing results, there is still a serious lack of knowledge regarding important aspects such as elastic properties, electronic band structure using advanced exchange correlation functional, charge density, and photocatalytic efficiency that must be addressed in order to take full advantages of CNO for potential technological applications.
In view of above circumstances, we explore structural, elastic, electronic, and photocatalytic properties of CNO. Investigating the effect of pressure on the aforementioned physical characteristics of CNO at low and high pressures is the main objective of this research.

Methodology
Using the CASTEP algorithm, the first principles calculations of CNO were performed within the framework of density functional theory (DFT) 29 using the plane wave pseudopotential approximation. Perdew-Burke-Ernzerhof (PBE) 30 form of generalized gradient approximation (GGA) was used to calculate the exchange correlation energy generated by the electrical interaction of core ions and valance electrons in order to optimize the shape of the material. It is well known that the GGA-PBE approximation underestimates bandgap values, therefore, the electronic calculations were also performed using hybrid approaches such as sx-LDA 31 . After evaluating numerous cut-off points (where the energy is least), 400 eV was chosen as the plane-wave cut-off energy for the calculations. For Brillouin zone sampling, a Monkhrost-pack grid 32 of 15 × 15 × 15 k-points was used. The calculation of the ground state atomic configuration were performed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach 33,34 with the ultrasoft pseudopotential method 35 . The ultrasoft pseudopotential approach carries out the calculations of the materials by treating the electron density in the valance as the soft portion and the core region as the hard part, where the cut-off energy is significantly decreased and the computational efficiency noticeably improves. The stress-strain method included in the CASTEP code was used to determine the bulk modulus, shear modulus, and single crystal independent elastic constants. To execute the pseudo-atomic calculations, the following electronic configurations were taken into consideration: 5s 2 5p 6 6s 1 for the Cs, 4s 2 4p 6 4d 4 5s 1 for the Nb atom, and 2s 2 2p 6 for the O atom. At the time of the geometry optimization, the energy convergence of the total energy, 0.5 × 10 −5 eV/atom, the maximum interatomic force, 0.01 eV/Å, the maximum stress, 0.02 GPa, and the ionic displacement, 5 × 10 −4 Å were set. CNO belongs to the cubic (space group Pm-3m ) crystal structure. The atomic positions for the Cs, Nb, and O atoms in the unit cell are (0, 0, 0), (0.5, 0.5, 0.5), and (0, 0.5, 0), respectively 36 .

Results and discussions
Structural properties. Figure 1a shows the 3D and 2D schematic illustration of cubic CNO crystal structure. By fitting the reduced total energy of the crystal with respect to the volume of the unit cell using the Birch-Murnaghan equation of state 15 , the geometry optimizations were carried out to find the lattice constants, isothermal bulk moduli, and pressure derivatives. The obtained value of a = 4.15 Å, which is very close to the reported data of CNO 17 that asserts the authenticity of the present calculation.
In order to investigate the pressure-dependent properties of CNO, the pressure dependent stability was checked. The calculated negative values of ground state energy of CNO reflects the stability of CNO up to 100 GPa. Figure 1b displays the pressure-dependent ground state energy of CNO. From Fig. 1b, it is seen that the minimum energy of CNO increase with increasing hydrostatic pressure. The rise in the ground state energy announces that the applied pressure drives the structure to be unstable and more energy is needed to stabilize the compound 37 . Figure 1c demonstrates the fluctuation of the lattice constant and unit cell volume with hydrostatic pressures up to 100 GPa. From graph, it is realized that the normalized lattice constant and unit cell volume gradually decrease with increasing hydrostatic pressure. As the pressure rises, the structure's relative compression reduces as a result of the inter-atomic repulsive interaction.
Stiffness constants and elastic moduli. The "strain-stress" approach, which was used in earlier investigations 33,34 , was used to perform the calculations of elastic constants. The three independent elastic stiffness constants C 11 , C 12 , and C 44 are obtained for CNO due to its cubic crystal structure. The pressure dependent fluctuations of C ij 's (i, j = 1, 2 & 4) which are shown in Table 2, and displayed in Fig. 2a.  www.nature.com/scientificreports/ The mechanical stability can be confirmed from the positively defined quadric form of energy density, where the coefficients obtained from DFT calculations (elastic stiffness) fulfill the cubic structure's fundamental minors and these are (C 11 -C 12 > 0), (C 11 + 2C 12 > 0) and C 44 > 0 32 . It is noticed that the elastic constants of CNO totally satisfy the aforementioned stability criteria for the entire range of applied hydrostatic pressure. Thus, CNO shows mechanical stability under pressure and the estimated elastic stiffness constant go under monotonous increase with increasing pressure.
The various elastic parameters, such as Y, B, G, and Poisson's ratio (ν) and hardness (H V ) were determined using the acquired elastic constants, C ij . By averaging the upper and lower bounds of Voigt's and Reuss's techniques, B and G have been calculated using the Voigt-Reuss-Hill approximation by the following equations: where, B R and G R indicate the Reuss approximation, B V and G V represent the Voigt approximation, and B and G have been calculated following the Voigt-Reuss-Hill approximation 38 .
Additionally, Y, ν and H V are the function of B and G and can be calculated from the following equations The calculated values of Y, B, and G under different pressure have been reported in Table 2. According to Table 1, the CNO has a large value of Y among the three elastic moduli (B, Y, and G) across the whole range of pressure. As the elastic tensor is directly proportional to Y, hence, the relatively large value of Y indicates that the CNO possesses a high elastic tensor. It can be also noticed that the elastic tensile resistance is getting increases with the increase of pressure and suggest the applicability of CNO at very high pressure.
Again, Y is inversely proportional to the critical thermal shock coefficient inside the elastic limit, which has an impact on a solid's thermal shock resistance 39 . Better thermal shock resistance is represented by a lower value of Y. The value of Y for LiNbO 3 40 , NaNbO 3 41 and KNbO 3 42 are 356, 272 GPa and 298 GPa respectively, whereas the obtained value for CNO is 271 GPa. As a result, CNO can be more suitable for thermal barrier coatings in comparison with above mentioned niobates. As demonstrated in Fig. 2b, it can be seen that G is less than B at  Fig. 3a and b. The Kleinman parameter (ξ) defied by ξ = C 11 +8C 12 7C 11 +2C 12 and essential parameter to determines the substantial contribution of the bond bending and bond stretching to minimize the external pressure effect whose value ranges from 0 to 1 46 . All the calculated values of ξ as shown in Fig. 3c forecast that CNO displays prominent bond bending over bond stretching at all external pressure.
The pressure dependent calculated values of Vickers Hardness of CNO have been listed in Table 2 and shown in Fig. 3d. A decreasing trend of hardness can be observed for the increasing pressure because the lower value of G/B and the larger value of Poisson's ratios are the indication of less hardness of the material and vice-versa 47 . The high value of H V predicts the CNO is a hard material and useful for mechanical applications.
The stress intensity factor K IC can be used to calculate the quantitative value at which a tiny break in the material starts to spread. A reliable model of fracture toughness was proposed by Niu et al. 44 and used the following empirical formula to calculate K IC : where V 0 is the volume per atom.
From the calculation, it can be seen that CNO possesses a high value of K IC in the whole range of pressure (Fig. 3f) i.e., the material can show high resistance to fracture propagation or micro cracks.
The machinability index, μ M (= B/C 44 ) 48 is important for determining how lubricating and plastic a solid is 49 . Figure 3e shows that the value of μ M increases in accordance with increasing pressure that proves the high-pressure applicability of CNO. In comparison to other materials, CNO 48 shows a greater value of μ M , which indicates excellent lubricating qualities and a reduced friction value that may be useful to design industrial machineries.
Electronic properties. We investigate the electronic band structure of CNO (Fig. 4) that describes the state of electrons in terms of their energy, E, and momentum, k. Figure 4 shows that CNO exhibits semiconducting nature with an indirect bandgap. In general, indirect bandgap semiconductors are utilized for photovoltaic device applications 17 .
This simulated bandgap is found to be fitting well with the prior theoretical value 13 . As it is well known that the GGA-PBE approach underestimates the bandgap values, therefore, we have performed the calculation using hybrid approaches such as sx-LDA since it gives the bandgap value close to the experimental results 31 . Interestingly, the bandgap value is enhanced significantly to 1.84 eV due to the use of sx-LDA (Fig. 4). Unfortunately, there is no available experimental data to compare the present result. The bandgap of CNO predicts the IR photodetector applications and substantiates the photoactive characteristics.  www.nature.com/scientificreports/ The electronic band structure also determines the dispersion relation for electrons in a material. The G-R direction shows the larger energy dispersion in comparison with X-R, R-M, and M-G directions for CNO. Consequently, it is believed that the band dispersion in the G-R direction controls the charge density 50 . Highly dispersive bands correspond to higher electrical conductivity due to their low carrier effective mass and higher charge mobility 51 . Figure 5a depicts the total and partial density of states of CNO to analyze the orbital contribution close to the Fermi level. As displayed in Fig. 5a, below the Fermi level (0 to − 6.9 eV), the valance band (VB) arises mainly from the contribution of 2p orbital of O atom, which is well-known for oxide-based semiconductor 52 . Strong hybridization among Cs-5p, Nb-4d, and O-2p orbitals is also observed in the top of VB. Besides, O-2p, and Nb-4d orbitals are mainly attributed to the bottom of the conduction band (CB). Cs-5p, Nb-4p orbitals also contribute to the upper CB.
The bandgap, preferred orientation, and thermoelectric characteristics of CNO are all significantly changes with the external pressure. The obtained values of E g using conventional GGA method at 0 and 100 GPa are 1.35 eV and 1.01 eV, respectively. On the other hand, when we use the hybrid functional like sx-LDA, the bandgap values at 0 and 100 GPa are 1.84 eV and 1.61 eV, respectively. The change of E g for GGA and sx-LDA are 0.34 eV and 0.23 eV which is very closed. However, it is well known that the hybrid functional gives more accurate value (closed to experimental result) of bandgap compared to conventional functional. A material to be a narrow bandgap semiconductor, the value of the bandgap should be near the infrared region. The obtained value of the bandgap using hybrid functional suggests that CNO can not be a narrow bandgap semiconductor at 100 GPa.
It can be seen from Fig. 5b that the bandgap of CNO increases up to 10 GPa and after that it begins to decrease with increasing pressure. Because electron-hole pairs become closer under pressure and their Coulomb interaction cannot be overlooked initially, the bandgap widens, leading to increase kinetic energy. Further increased pressure with increasing kinetic energy, causing the change in electron/hole-ion potential, makes the material able to neglect the Coulomb interaction and impose the electronic state to be closer. As a result, the E g decreases later with the increasing pressure. This observation is well agreed with recent theoretical report 28 , however, the authors do not describe the phenomena below 10 GPa.
Mulliken population analysis provides details on the charge, bond length, and bond population in a solid crystalline system, which aids in figuring out how charges are distributed among the bonds as well as ionicity and covalency of a material. The bonding and antibonding states, respectively, are responsible for the positive and negative bond overlap populations. The calculated data of charge, population, and bond length under pressure of CNO have been reported in Table 3.  Table 3, it can be seen that with increasing pressure the covalency of Nb-O bond is decreased. In contrast, the antibonding character of the Cs-O bond is becoming weaker as the applied pressure give rise to the bond populations and reduces the charge of the Cs atom.
Understanding the type of atomic bonding in a compound can be done by looking at the contour map of the electron charge distribution among the atoms that make up the compound. Figure 6a-d show the contour color map of CNO at 0, 20, 40, 60, 80 and 100 GPa. The electron cloud that has been generated by the charge distributions around the atoms is almost spherical, and its intensity controls how much charge is accumulating. The antibonding nature can be explained from the correlation of DOS, band structure and CDD map. In the band structure, it is seen that the dispersion curve in the valence band is flat at a finite wave vector. It indicates the valance band to be occupied by the electrons with same wave vector and in CNO, electrons of Cs-5p, O-2p orbitals are responsible which are observed from partial density of states (Fig. 5). With the same wave vector, the wave functions of the electrons from different orbital interfere each other. From the Pauli's exclusion principal, if two electrons try to share an identical set of quantum numbers, their probability functions cancel (destructive interference) and create zero electron probability density between the orbitals. As a result, from CDD, we observe the antibonding nature of Cs-5p and O-2p orbitals. On the other hand, due to the constructive interference of the wave functions of Nb-4d and O-2p suggest the bonding nature.
Effective mass and photocatalytic activity. To expand light absorption into the visible area and effectively use the solar energy, an efficient photocatalyst needs a bandgap energy less than 3 eV 53 . The bandgap of the semiconducting CNO proves that it can absorb a wide range of solar radiation. In Fig. 7, E ph represents the  www.nature.com/scientificreports/ energy of the photon and the E ph needs to be greater than E g . The indirect bandgap (Fig. 4) may be more advantageous for photocatalytic applications because it may lower the radiative recombination rate due to the momentum mismatch between the CBM and VBM, which is advantageous for a longer carrier lifetime and therefore, photocatalytic activity 54 . The band structures in Fig. 4 also make it clear that the CBM of CNO is more parabolic (highly dispersive) than the VBM. This suggests that the photogenerated electron may have a lower effective mass than the hole effective mass. In present work, the low values of m * e and m * h imply that it has high electrical conductivity. The photogenerated carriers can quickly transfer to the surface of CNO, which is crucial for photocatalytic activity. Nevertheless, the low value of hole carrier effective mass (2.63m e for GGA-PBE) has a great impact on catalytic efficiency. The low value of carrier effective mass of the hole causes the highest rate of H 2 production. In addition, relatively high ratio of electron ( m * e ) to hole ( m * h ) effective mass is associated with easy separation of photogenerated electrons from their associated holes, which lowers the probability of their recombination and increases their availability to perform catalytic processes. This is because a decrease in carrier mass results in a corresponding increase in carrier mobility. Therefore, the reduction of recombination of the electron-hole carrier of CNO enhances its photocatalytic efficiency.
In order to clarify the separation of photogenerated electron-hole pairs over the CNO, it is necessary to find out the conduction and valence band edge potentials of the component. In the case of water splitting, the valence band edge potential should be more positive than the potential needs for oxygen evolution (1.23 eV vs. NHE) and the conduction band potential should be more negative than the potential corresponding to the hydrogen evolution reaction (0 eV vs. NHE). These energy band potentials are calculated using the following empirical equations 59 : where, χ is the absolute electronegativity of CNO and the E CB and E VB indicate the band edge potentials of CB and VB, respectively. The Mulliken electronegativity of an atom is determined by the average value of its electron affinity and its first ionization energy 60 . E g denotes the acquired electronic bandgap, while E e resembles the energy of free electrons on the hydrogen scale (4.5 eV).
The CNO has an estimated electronegativity, χ of 5.12 eV. Figure 8a and b show the band edge potentials of VB and CB in CNO for the GGA-PBE, and sx-LDA approximations. The thermodynamic aspect of the CBM potential of CNO, which is negative, demonstrates that H + to H 2 reduction will occur which could delay the electron-hole recombination process. As the dilation in the recombination process enhances the photocatalytic efficiency, the negative value of CB potential substantiates the CNO to be a good photocatalytic material. The evolution of O 2 from water is revealed by the VBM potential, which is higher than O 2 /H 2 O (1.23 eV) in all approaches. The larger www.nature.com/scientificreports/ value of the VBM potential of CNO indicates the possibility of a spontaneous photocatalytic reaction. Therefore, the VBM potential also proves the CNO is good for water splitting applications. The band edge potentials that characterize the photocatalytic activity are greatly influenced by the bandgap as shown in Fig. 8c. With increasing pressure, the CB potential initially decreases (becomes more negative) and then increase (after 10 GPa) and exits the potential of hydrogen evaluation reaction i.e., the CNO losses its photocatalytic efficiency. The change of VB potential under pressure also displays a similar effect on photocatalytic activity. The change in the bandgap, E g is responsible for these changes. However, from these calculations, it can be confirmed that at 10 GPa CNO shows the highest photocatalytic efficiency and at high pressure, it stops functioning as a photocatalyst.

Conclusions
Using the state of art density functional theory, we investigate the effect of hydrostatic pressure on the structural, elastic, electronic, and photocatalytic properties of CsNbO 3 . The values of Pugh's ratio, Poisson's ratio, Cauchy pressure, and Kleinman parameter confirmed the ductile nature below 20 GPa. The obtained high value of fracture toughness and machinability index revealed the good mechanical application against micro-cracks and excellent lubricating qualities. The electronic band structure discloses the semiconducting character of the compound. Two different approaches provide variety in bandgap energy of 1.35 and 1.87 eV for GGA-PBE, and sx-LDA, respectively. The estimated indirect bandgap suggests the good photoactive character of CsNbO 3 . Under pressure, the bandgap energy increases initially till 10 GPa and then decreases gradually with pressure. The calculated Mulliken effective charge, bond population and bond length revel the good covalency and antibonding character of Nb-O and Cs-Nb, respectively. The calculation of electron charge density was in good agreement with the Mulliken population analysis. Low value of carrier effective mass assert that CsNbO 3 has to be good electrical conductivity as well as photocatalytic activity. The calculated band edge potentials revealed the CNO would exhibit excellent water splitting efficiency. The result of the current computations are expected to serve as a foundation for future experimental and theoretical investigations of the suitability of CsNbO 3 in various device applications.